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Fixed-Point Theory on a Frechet Topological Vector Space
Joint Authors
Ben Amar, Afif
Cherif, Mohamed Amine
Mnif, Maher
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-04-07
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
We establish some versions of fixed-point theorem in a Frechet topological vector space E.
The main result is that every map A=BC (where B is a continuous map and C is a continuous linear weakly compact operator) from a closed convex subset of a Frechet topological vector space having the Dunford-Pettis property into itself has fixed-point.
Based on this result, we present two versions of the Krasnoselskii fixed-point theorem.
Our first result extend the well-known Krasnoselskii's fixed-point theorem for U-contractions and weakly compact mappings, while the second one, by assuming that the family {T(⋅,y):y∈C(M) where M⊂E and C:M→E a compact operator} is nonlinear φ equicontractive, we give a fixed-point theorem for the operator of the form Ex:=T(x,C(x)).
American Psychological Association (APA)
Ben Amar, Afif& Cherif, Mohamed Amine& Mnif, Maher. 2011. Fixed-Point Theory on a Frechet Topological Vector Space. International Journal of Mathematics and Mathematical Sciences،Vol. 2011, no. 2011, pp.1-9.
https://search.emarefa.net/detail/BIM-468348
Modern Language Association (MLA)
Ben Amar, Afif…[et al.]. Fixed-Point Theory on a Frechet Topological Vector Space. International Journal of Mathematics and Mathematical Sciences No. 2011 (2011), pp.1-9.
https://search.emarefa.net/detail/BIM-468348
American Medical Association (AMA)
Ben Amar, Afif& Cherif, Mohamed Amine& Mnif, Maher. Fixed-Point Theory on a Frechet Topological Vector Space. International Journal of Mathematics and Mathematical Sciences. 2011. Vol. 2011, no. 2011, pp.1-9.
https://search.emarefa.net/detail/BIM-468348
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-468348